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Q29.

Expert-verified
Found in: Page 73

Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776

Use the distributive property to write an equivalent variable expression.$3 \left( y + 9 \right)$

$3 \left(y+9\right)= 3y + 27$.

See the step by step solution

Step-1 – What are real numbers?

Real numbers are simply the combination of Whole numbers, Integers, Rational and Irrational numbers in the number system.

Step-2 – Distributive Property of Multiplication

Suppose a, b, and c is three real numbers.

Distributive Property of Multiplication

Property: $\text{a} \text{(b} \text{+} \text{c} \text{)} = \text{a} · \text{b} + \text{a} · \text{c}$

Example: $\text{12} \text{(3} \text{+} \text{4} \text{)} = \text{12} · \text{3} + \text{12} · \text{4} = 36 + 48 = 84$

Step-3:  Evaluate the expression using the distributive property.

Distributive Property of Multiplication

Property: $\text{a} \text{(b} \text{+} \text{c} \text{)} = \text{a} · \text{b} + \text{a} · \text{c}$

$\begin{array}{l}3\text{\hspace{0.17em}\hspace{0.17em}}\left(y+9\right)=\text{\hspace{0.17em}\hspace{0.17em}}3\text{\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}}y\text{\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}}3\text{\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}}9\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}3y\text{\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}}27\text{\hspace{0.17em}}\\ 3\text{\hspace{0.17em}\hspace{0.17em}}\left(y+9\right)=\text{\hspace{0.17em}\hspace{0.17em}}3y\text{\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}}27\end{array}$